TMDB's API lives at https://api.themoviedb.org/3. Poster and backdrop paths are relative — prefix them with https://image.tmdb.org/t/p/w500.
Sign up and request an API key under Settings → API, then use the API Read Access Token as Authorization: Bearer <token>. In the examples it's written {{TMDB_TOKEN}}.
Full reference: https://developer.themoviedb.org/reference/intro/getting-started
curl "https://api.themoviedb.org/3/search/movie?query=inception" \
-H "Authorization: Bearer {{TMDB_TOKEN}}"27205 is Inception.
curl https://api.themoviedb.org/3/movie/27205 \
-H "Authorization: Bearer {{TMDB_TOKEN}}"curl https://api.themoviedb.org/3/trending/all/week \
-H "Authorization: Bearer {{TMDB_TOKEN}}"